document.write( "Question 1204923: The rate of return for firms on the stock market is normally distributed with a 5% average rate and standard deviation of 2%. What rate of return would put a firm in the top 20%. Please show steps \n" ); document.write( "

Algebra.Com's Answer #841499 by ikleyn(52879) $\"\"$ $\"About$

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\n" ); document.write( "The rate of return for firms on the stock market is normally distributed
\n" ); document.write( "with a 5% average rate and standard deviation of 2%.
\n" ); document.write( "What rate of return would put a firm in the top 20%. Please show steps
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document.write( "They want you determine a raw mark on x-axis such that the area\r\n" );
document.write( "under this normal curve on the right from this raw mark be exactly 20%, or 0.05.\r\n" );
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document.write( "For it, you may use the standard function invNorm of your regular calculator TI-83/84.\r\n" );
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document.write( "The format of this function is  raw mark = invNorm(area, mean, SD).\r\n" );
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document.write( "So, you write  raw mark = invNorm(0.95, 0.05, 0.02).\r\n" );
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document.write( "Here first  value \"0.95\" denotes the area under the normal curve on the left of the raw mark; \r\n" );
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document.write( "     second value \"0.05\" denotes the 5% = 0.05 mean;\r\n" );
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document.write( "     third value  \"0.02\" denotes standard deviation of 2% = 0.02.\r\n" );
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document.write( "Doing this way, you get raw mark = 0.083  (rounded).\r\n" );
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document.write( "      We write 0.95 for the first argument, because the function invNorm\r\n" );
document.write( "      takes/accepts as the first argument the area on the LEFT of the raw mark 0.95 = 1 - 0.05.\r\n" );
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document.write( "Thus, the rate of return must be at least 0.083, or 8.3% in order for the firm be in the top 20%.\r\n" );
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document.write( "Alternatively, instead of using your regular calculator TI-83/84, you may use online \r\n" );
document.write( "(free of charge) calculator at this web-site\r\n" );
document.write( "https://davidmlane.com/hyperstat/z_table.html\r\n" );
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document.write( "This online calculator has intuitively clear interface and shows the area of interest,\r\n" );
document.write( "so you never will make mistake and will clearly understand what you are doing and why.\r\n" );
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document.write( "Use this online calculator in the \"Value from area\" mode.\r\n" );
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document.write( "This online calculator is a perfect teacher, so, if you are a beginner student in such calculations, \r\n" );
document.write( "you will learn the subject QUICKLY.\r\n" );
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document.write( "Therefore, I advise you to start using this online calculator. Later, as you gain a necessary experience,\r\n" );
document.write( "you may return to regular calculators TI-83/84.\r\n" );
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